1. The Schwarzschild black hole is the simplest ideal black hole: i.e., black hole NOT affected by perturbations. (Actually, all real black holes are affected by perturbations to one degree or another.) The Schwarzschild black hole has zero angular momentum. and zero electric charge. Its structure is entirely determined by its mass and it is exactly spherically symmetric.

  2. Virtually all astronomical objects have rotation because the processes of formation virtually always have inward swirl, NOT a straight in radial, collapse. There the ideal Schwarzschild black hole probably NEVER occurs.

    However, Kerr black holes (i.e., rotating black holes) when rotating slowly enough approximate Schwarzschild black holes.

  3. Kerr-Newman black holes are those with NON-ZERO angular momentum and net electric charge (Shapiro & Teukolsky 1983, p. 357).

    Usually, macroscopic bodies in the universe are nearly neutral because any charge imbalance quickly attracts neutralizing charge. Thus, black holes that show significant Kerr-Newman black hole behavior seemed unlikely to exist. However, since circa 2015, it is hypothesized that Kerr-Newman black holes do exist and may have observable effects: e.g., as the sources of some fast radio bursts (FRBs) (see, e.g., Liu et al. 2016). So there may be mechanisms to significantly charge black holes and keep them charged.

  4. In fact, all real black holes to some degree or other can be modeled as Schwarzschild black holes.

  5. The black hole singularity (which is a gravitational singularity) at the center of the Schwarzschild black holes is a point of infinite density and finite mass (i.e., a "real" point mass).

    In fact, the black hole singularity probably does NOT exist. Quantum gravity effects (NOT included in general relativity) probably prevent the existence of gravitational singularities. But probably some super-dense state of mass-energy exists at the center of black holes---perhaps it has something like the Planck density ρ_Planck = c**5/(G**2*ħ) = 5.15500*10**93g/cm**3.

  6. The event horizon is located at the Schwarzschild radius R_sch = 2GM/c**2 = (2.9532 km)*(M/M_☉) = (19.741 AU)*[M/(10**9*M_☉)].

    The event horizon is the point of no return. Nothing can escape from within the event horizon, NOT even light.

    The light rays in the diagram start from vanishingly close to the event horizon, NOT within it. From within it, there is NO path out (see Wikipedia: Event horizon: Event horizon of a black hole).

    The diagram shows that the non-radial outgoing light rays will be gravitational lensed back to the event horizon and they will NEVER emerge.

    A outgoing nearly radial light rays will be gravitational redshifted by reaching infinity to nearly to zero photon energy E=hν

  7. Note the event horizon is, in fact, the defining characteristic of black holes no matter what theory of gravity is the true macroscopic emergent theory of gravity, general relativity or something better that we know NOT of yet.

  8. The curvature of space outside the event horizon is such that relative to the Schwarzschild black holes center change in circumference is smaller than change in radius: i.e., ΔC < 2πΔr. As you go to infinity, you recover the Euclidean geometry ΔC = 2πΔr.

    Note the referred to distances are what you measure with a rigid ruler at one instant in time.

    What of the curvature of space inside the event horizon? Let's NOT worry about that now.

  9. For reference, the Schwarzschild radius formulae are given below (local link / general link: black_hole_schwarzschild_radius_formulae.html):


  10. See Black hole keywords below (local link / general link: black_hole_keywords.html):